Irritations in Introductory Physics:

The Pulley Problem

I see a lot of introductory physics textbooks, and by and large they all follow the same format, treat the topics in the same order and feature the same type of problems for the student to practice on. There is a variation in the sophistication of the mathematics, whether algebra-based (easier) or calculus based (more challenging), but essentially, the same types of problems are posed.

One class of problem, which always crops up in the chapter on Force and Newton’s Laws, is the pulley problem. When you hold a rope taut, the force exerted on the rope is known as the tension force. This force is also exerted on whatever the other end of the rope is attached to. The pulley is merely a device that changes the direction that the tension force is exerted. The student is then faced with a network of pulleys and ropes, and is asked to find some unknown force somewhere in the system.

https://commons.wikimedia.org/wiki/File%3APower_Pulley_FBD.jpg

As you can see, some of the given arrangements are quite complicated! I also look at that picture and think “I have absolutely no interest whatsoever in solving that problem, even as a kind of intellectual challenge”. And if I’m thinking that, what must a student be thinking. Panic? Terror? Not exactly going to encourage people to enjoy their physics, is it? As a physicist friend once remarked to me “Students must think that physicists have these complicated sets of pulleys in their offices and spend all day pulling strings”. And we don’t. Usually.

What do I have against these types of problems? They aren’t very realistic. The vast majority of students will never encounter anything remotely as complicated, or ever have to calculate forces within such a system. It’s just not a relevant skill for most of the class. There is a methodology to solve the problems, which once you know it, enables any problem to be solved, with varying degrees of tedium and requiring various amounts of mathematics. Testing if you know the methodology can be done with a relatively simple example, the rest is simply grinding out algebra. It does very little for understanding of physics. That’s why I don’t set many of these problems, and they are considerably shorter than the one pictured above!

There is one example which I do set, and that is where a patient with a broken limb has it held in traction.

https://commons.wikimedia.org/w/index.php?search=traction+orthopedics&title=Special:Search&go=Go&uselang=en&searchToken=8tvd1byegtbnclvqaofh7vc9y#/media/File:Postoperative_treatment;_an_epitome_of_the_general_management_of_postoperative_care_and_treatment_of_surgical_cases_as_practised_by_prominent_American_and_European_surgeons_(1907)_(14598502449).jpg

You notice that the system is usually rather simple, and the objective is obvious — keep the limb under some tension whilst the healing process goes on. This makes it a problem that the students can see the point of solving. And that motivation is extremely important, especially for students who aren’t taking physics for the joy of it.

I could leave the traction problem above unsolved by using the old “And I leave this as an exercise for the student” ruse. This used to annoy me immensely when I was a student, so I won’t do that to you, dear reader. In this case, provided that the string has a low weight compared to the hanging weight, then the tension force on the leg is due to the force of gravity on the hanging mass (the weight of the weight, in fact). Each of the pulleys is merely turning that tension force through 90 degrees, so that it is exerted on the leg of the patient, pulling the leg up.

So there you have pet peeve number one, and how to work around it.

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